How Lenses Work

A piece of glass that controls light

A lens is a carefully shaped piece of transparent material — usually glass or plastic — with at least one curved surface. That curve is no accident. By grinding the glass into the right shape, we can make light bend in exactly the way we want, gathering it to a sharp point or fanning it out. Lenses sit at the heart of spectacles, cameras, telescopes, microscopes, projectors, phone cameras, and even your own eyes. Once you understand how a lens steers light, you understand a huge slice of everyday technology.

Everything a lens does comes from one idea you may already know: refraction, the bending of light when it changes speed. If you would like a refresher on why light bends at all, look back at reflection and refraction of light.

Why a lens bends light

Light travels fast in air but more slowly inside glass. When a ray crosses from air into glass at an angle, it bends; when it leaves the glass back into air, it bends again. On a flat window the two bends cancel out and light passes straight through. But a lens has curved surfaces, so different parts of a wide beam strike the glass at different angles and bend by different amounts.

Imagine a beam of parallel rays — like sunlight — hitting a lens that bulges in the middle. The rays near the top get bent downward, the rays near the bottom get bent upward, and the central ray goes straight through. The clever shape of the curve makes all of them cross at the same point. That is how a lens focuses light: it is just refraction, organised by geometry.

Convex lenses: bringing light together

A convex lens bulges outward and is thickest in the middle. It is also called a converging lens because it brings parallel rays together. The spot where those rays meet is the focal point, and the distance from the centre of the lens to the focal point is the focal length (often written f).

A fatter, more strongly curved lens bends light harder, so it has a short focal length. A flatter lens bends light gently and has a long focal length. This single number tells you almost everything about how the lens behaves.

Convex lenses do two different jobs depending on how far the object is:

• Object far away (beyond the focal point): the lens makes a real image that is upside down and can be caught on a screen. This is how a camera lens throws a picture onto its sensor and how a projector casts a film onto a wall.
• Object very close (nearer than the focal length): the lens makes an enlarged, upright virtual image. This is the magnifying glass: the rays never actually meet, but your brain traces them backward and sees a big, magnified object.

Concave lenses: spreading light out

A concave lens is the opposite shape — thinner in the middle, like a cave hollowed out of the glass. It is a diverging lens because it spreads parallel rays apart so they fan outward as if coming from a single point behind the lens. That point is the virtual focal point.

A concave lens always makes an image that is upright and smaller than the object. On its own it cannot focus light onto a screen, but it is exactly what a short-sighted person needs. Their eye focuses light too soon; a concave lens spreads the rays a little first so the eye then focuses them correctly on the retina.

Real images and virtual images

This pair of words is worth getting straight, because it is the key to using lenses.

• A real image forms where light rays actually cross. You can place a screen there and catch the picture. Real images from a single convex lens are upside down. Cinema screens, camera sensors, and the image on the back of your eye are all real images.
• A virtual image forms where rays only appear to come from. The rays never truly meet, so you cannot project it on a screen — you can only see it by looking through the lens. The enlarged view in a magnifying glass is a virtual image.

Worked example: finding the focal length

Physicists link the object distance (u), the image distance (v) and the focal length (f) with the thin-lens equation:

1/f = 1/v − 1/u

Let's keep it simple with a clean case. A convex lens forms a sharp, focused image of a distant tree on a wall. Because the tree is very far away, its light arrives almost perfectly parallel, so the image forms right at the focal point. You measure the distance from the lens to the wall as 20 cm.

The image of a distant object forms at the focal point. Therefore the focal length f = 20 cm.

Now suppose you label this same lens "+5 dioptres". A lens's power in dioptres is simply:

Power (D) = 1 ÷ focal length in metres Power = 1 ÷ 0.20 m = 5 D ✓

The numbers agree. Stronger lenses (higher dioptres) have shorter focal lengths and bend light more sharply — which is why an optician describes your glasses in dioptres.

Lenses everywhere

• The eye has a flexible convex lens that changes shape to focus near and far objects onto the retina.
• A camera uses convex lenses to throw a real, upside-down image onto its sensor (software flips it for you).
• A microscope and a telescope each combine two or more lenses, one to gather light and one to magnify the result.
• Glasses correct vision: convex lenses for long-sight, concave lenses for short-sight.

Try it yourself! 🧪

Make a real image with a magnifying glass. You will need a magnifying glass (a convex lens), a sheet of white paper, and a bright window — ideally a sunny day, but a bright lamp across the room also works. In a dimmed room, hold the lens up so it faces the window. Hold the paper behind the lens and slowly move it closer and further until a small, sharp picture of the window — trees, buildings, the sky outside — snaps into focus on the paper. Look carefully: the image is upside down. You have just created a real image, exactly the way a camera does. Measure the distance from the lens to the paper when the image is sharpest: because the window is far away, that distance is close to the lens's focal length.

Safety first: focus the lens onto paper, never toward anyone's eyes, and never use a lens to focus the Sun onto skin, dry leaves, or anything that could burn — a convex lens concentrates sunlight enough to start a fire. Do the experiment indoors with an adult nearby.

By moving the paper you can feel how the lens has one special distance where light comes together. That distance — the focal length — is the single most important fact about any lens.